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a b s t r a c tFor integers k, r > 0, a (k, r)-coloring of a graph G is a proper k-coloring c such that for any vertex v with degree d(v), v is adjacent to at least min{d(v), r} different colors. Such coloring is also called as an r-hued coloring. The r-hued chromatic number of G, χ r (G), is the least integer k such that a (k, r)-coloring of G exists. In this paper, we proved that if G is a planar graph with girth at least 6, then χ r (G) ≤ r + 5. This extends a former result in Bu and Zhu (2012). It also implies that a conjecture on r-hued coloring of planar graphs is true for planar graphs with girth at least 6.

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